Yes, both C1 and C2 are charged with 1/2 wave power (one pulse every
full cycle). However, it appears to me that the difference is that
they only discharge during one half-cycle of every full cycle. On the
charging half-cycle they are not also discharging, but they only
discharge on the opposite half-cycle. This is different from the 2x2
doubler, where both caps are charged on alternate half-cycles, but both
caps discharge during the entire full cycle. If I've analysed this
correctly, it seems that there should be some improvement in voltage
regulation over the 2x2. But I wanted others to look at the circuit
and offer their ideas on it as well.

73,
Mike, KK6GM